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# Mathematics

Mathematics is a creative, dynamic system that we use to model and understand our environment. Math students at Pacifica will be taught to appreciate the aesthetics and beauty of mathematics and will gain a deep understanding of how it enriches their lives. They will be challenged to gain not only a conceptual understanding of mathematical skills and principles, but also knowledge of, and experience with, pure reasoning. This logical reasoning will prepare the students for a broad range of situations in which answers to real life problems can be found with accuracy. The students will see the interdependence of mathematics and music, art, architecture, science, and philosophy to other disciplines and will become lifelong students of mathematics regardless of the career they pursue.

## Math Courses

**Graduation requirement: 3 years of high school math**

### Algebra 1

**(Year Course)UC Approved**

This course is designed to develop a student’s mathematical comprehension and skills. Special attention is given to the solution of linear equations and inequalities, solution of quadratic equations, evaluation of algebraic expressions, performance of polynomial arithmetic, operations with rational expressions, operations with radicals, and the solution of graphing of linear equations involving two variables. The analysis and solution of word problems is stressed throughout the course. *A TI-84PLUS graphing calculator is required for this course.*

### Geometry

**(Year Course)UC Approved**

*Prerequisite: Completion of Algebra 1*

This course presents geometry as a topic of importance for daily living, for career development, and for the future study of mathematics. It applies the skills of drawing, measurement, visualization and deductive logic to the study of triangles, quadrilaterals, general polygons, and circles. It analyzes concepts of similarity, congruence, and isometric transformations of figures. Emphasis is placed upon the analysis of right triangle and the area and volume of plane and solid figures. Trigonometry of right triangles is introduced. Techniques of coordinate geometry are developed. Algebraic representation and deductive analysis of geometric relations are stressed throughout the course. A TI-84PLUS graphing calculator is required for this course.

### Algebra 2

**(Year Course)UC Approved**

*Prerequisite: Completion of Geometry*

Algebra is the study of generalized arithmetical operations. The Algebra 2 course is an extension of the Algebra 1 curriculum; topics that were first introduced in Algebra 1 will be built upon and applied to problems that require higher order thinking skills. A primary goal of Algebra 2 is for students to conceptualize, analyze, and understand functions. Students will investigate and learn about linear, absolute value, radical, quadratic, exponential, logarithmic functions, along with conic sections and mathematical sequences and series. Students will be required to think and communicate verbally, algebraically, numerically, and graphically as they face the challenge to develop conceptual understanding, quantitative reasoning, and problem-solving skills in addition to mathematical procedural skills. Students will use technology such as graphing calculators and computers on a regular basis. A TI-84PLUS graphing calculator is required for this course.

### Pre-calculus

**(Year Course)UC Approved**

*Prerequisite: Completion of Algebra 2 with a grade of C or better*

The first semester of Pre-calculus is devoted to the study of Math Analysis. This part of the course lays the foundation for Calculus by surveying the behavior of the most common functions and relations and their inverses, including conics, powers, exponential, logarithmic and trigonometric functions. The course explores ways of handling the graphs, tables, and formulas that represent the functions. Students are expected to read graphs and think graphically, and to read tables and think numerically. They have the opportunity to apply these skills along with their algebraic skills to many applications and to modeling real-world problems, including data analysis and regression equations. Graphing utilities are used extensively. Second semester is devoted to the study of Trigonometry. Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. *A TI-84PLUS graphing calculator is required for this course.*

### Honors Pre-Calculus

**(Year Course)UC Approved**

*Prerequisite: Completion of Algebra 2 with a grade of a B+ or better and instructor approval.*

The first semester of Pre-calculus is devoted to the study of Math Analysis. This part of the course lays the foundation for Calculus by surveying the behavior of the most common functions and relations and their inverses, including conics, powers, exponential, logarithmic and trigonometric functions. The course explores ways of handling the graphs, tables, and formulas that represent the functions. Students are expected to read graphs and think graphically, and to read tables and think numerically. They have the opportunity to apply these skills along with their algebraic skills to many applications and to modeling real-world problems, including data analysis and regression equations. Graphing utilities are used extensively. Second semester is devoted to the study of Trigonometry. Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. Honors students will work at an accelerated pace with the expectation of self-motivation in preparation for advanced placement. Students will complete one research project. *A TI-84PLUS graphing calculator is required for this course.*

### AP Calculus AB

**(Year Course)UC Approved**

*Prerequisite: Minimum grade of a B in Pre-calculus or Honors Pre-calculus and instructor approval*

This course is designed to prepare the student to take the Advanced Placement Calculus AB Examination. Topics covered in AP Calculus AB include: algebraic, trigonometric, exponential and logarithmic functions, limits and continuity, the derivative and applications of the derivative, the antiderivative, the definite integral and applications and techniques of integrals. *A TI-84PLUS graphing calculator is required for this course.*

### AP Calculus BC

**(Year Course)UC Approved**

*Prerequisite: Minimum grade of a B+ in Honors Pre-calculus and instructor approval.*

This course is designed to prepare the student to take the Advanced Placement Calculus BC Examination. Topics covered in AP Calculus BC include: algebraic, trigonometric, exponential and logarithmic functions, limits and continuity, the derivative and applications of the derivative, the antiderivative, the definite integral, applications and techniques of integrals, sequences and series; parametric equations; polar coordinates, and vectors in the plane. *A TI-84PLUS graphing calculator is required for this course.*

### AP Statistics

**(Year Course)UC Approved**

*Prerequisite: Minimum grade of a B in Pre-calculus or a B or Honors Pre-calculus and instructor approval.*

This course is designed to prepare the student to take the Advanced Placement Statistics Examination. Students who pass the College Board Advanced Placement Exam in May, may earn one semester of college credit. Topics covered in AP Statistics include: exploring data/observing trends, planning a study, probability, and using statistical inference to predict. This course will require meetings outside of the normal class time arranged by the teacher. *A TI-84PLUS graphing calculator is required for this course.*